Vol. 12, No. 8, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
On the relative Galois module structure of rings of integers in tame extensions

Adebisi Agboola and Leon R. McCulloh

Vol. 12 (2018), No. 8, 1823–1886
Abstract

Let F be a number field with ring of integers OF and let G be a finite group. We describe an approach to the study of the set of realisable classes in the locally free class group Cl(OFG) of OFG that involves applying the work of McCulloh in the context of relative algebraic K theory. For a large class of soluble groups G, including all groups of odd order, we show (subject to certain mild conditions) that the set of realisable classes is a subgroup of Cl(OFG). This may be viewed as being a partial analogue in the setting of Galois module theory of a classical theorem of Shafarevich on the inverse Galois problem for soluble groups.

Keywords
Galois module structure, realisable classes, rings of integers, inverse Galois problem, relative K-group.
Mathematical Subject Classification 2010
Primary: 11R33
Secondary: 11R32, 11R65, 19F99
Milestones
Received: 28 August 2015
Revised: 23 March 2018
Accepted: 2 July 2018
Published: 4 December 2018
Authors
Adebisi Agboola
Department of Mathematics
University of California, Santa Barbara
CA
United States
Leon R. McCulloh
Department of Mathematics
University of Illinois
Urbana, IL
United States